Question: Solve for $x$ : $3\sqrt{x} + 8 = 10\sqrt{x} + 9$
Subtract $3\sqrt{x}$ from both sides: $(3\sqrt{x} + 8) - 3\sqrt{x} = (10\sqrt{x} + 9) - 3\sqrt{x}$ $8 = 7\sqrt{x} + 9$ Subtract $9$ from both sides: $8 - 9 = (7\sqrt{x} + 9) - 9$ $-1 = 7\sqrt{x}$ Divide both sides by $7$ $\frac{-1}{7} = \frac{7\sqrt{x}}{7}$ Simplify. $-\dfrac{1}{7} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.